Finite amplitude folding of single layers: elastica,bifurcation and structural softening

The amplification of viscous single-layer folds, from infinitesimal amplitudes up to finite amplitudes and large strains, is investigated analytically. Analytical solutions for finite amplitude folding of viscous layers valid for large viscosity contrasts and for post-buckling of elastic columns are shown to be identical. The failure of the classical, exponential amplification solution for folding is quantified using a nonlinear amplification equation similar to the Landau equation. The evolution of fold amplitude–strain for single layers with different initial amplitudes and viscosity contrasts essentially depends on a single parameter rather than three parameters as commonly assumed (strain, initial amplitude and viscosity contrast). This single parameter is constructed by scaling the strain with the crossover strain, which is the specific value of strain at which the linear solutions fail. Scaling the strain with the crossover strain yields a collapse of all amplitude evolution paths for different initial amplitudes and viscosity contrasts onto a single amplification path. Analytical solutions for the evolution of the layer-parallel deviatoric stress within the layer during folding are presented showing a decrease of the layer-parallel deviatoric stress with increasing fold amplitude. All stress–amplitude evolution paths for different initial amplitudes and viscosity contrasts can be collapsed onto a single stress–amplitude evolution path, if the amplitude is scaled by the crossover amplitude. The decrease in stress is proportional to a decrease in effective viscosity of the layer during folding. This decrease in effective viscosity represents structural softening, because the true, Newtonian viscosity of the layer remains constant.     

The magnetic resonance in high-temperature superconductors: evidence for an extended s-wave pairing symmetry

We have identified several important features in the neutron scattering data of cuprates that are difficult to explain in terms of d-wave and isotropic s-wave order parameters. Alternatively, we show that the neutron data are in quantitative agreement with an order parameter that has an extended s-wave (A_1g) symmetry and opposite sign in the bonding and antibonding electron bands formed within the Cu₂O₄ bilayers. The extended s wave has eight line nodes and changes sign when a node is crossed. This A_1g pairing symmetry may be compatible with a charge-fluctuation-mediated pairing mechanism.     

Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.     

Invariant Foliations and Decoupling of Non-autonomous Difference Equations

In this paper, we continue a previous study of the geometric properties of a certain prototype system of nonautonomous difference equations. In fact, we show that by means of the fundamental theorem on the existence of invariant fiber bundles two foliations of the extended state space can be found. This detailed information about the geometric structure of the underlying system is then used to construct transformations establishing the topological equivalence between a given coupled and a completely uncoupled system.     

Asymptotic behaviour and stability to linear non-autonomous neutral delay difference equations

This paper is concerned with the asymptotic behaviour and the stability of a class of linear neutral delay difference equations with variable coefficients and constant delays. Via an appropriate solution of the so-called generalized characteristic equation, an asymptotic criterion and a stability result are established.     

Monotone Solutions of Neutral Difference Equations of Odd Order

A class of monotone sequences is introduced. A classification of all such monotone solutions of odd order neutral difference equation is established. Necessary and/or sufficient conditions are then derived for the existence of these solutions.     

XPS Study of a Cu-A1-O Compound Under H2/CO Mixture

Mixed copper aluminium oxide has been studied by XPS. It was shown that the reduction under hydrogen of the precursor oxide leads to the formation of cuprous ions located in the octahedral sites of the spinel matrix γ-A1₂0₃ and hydridic species stored in the solid. The use of the pre-reduced compound at 300°C before catalysis with H₂/CO is necessary to maintain almost intact the spinel phase despite the formation of metallic copper, whereas a strong modification of a surface composition was obseved when the solid is directly treated by H₂/CO mixture.